When the login screen loops repeatedly and/or an "error logging into Facebook" message comes up, close out of everything and reboot your phone. It should connect just fine after that. (Related to device-specific memory limitations)

This could be a problem with your network provider and likely has nothing to do with your or your friend's device. For Droid phones, some have a known memory limitation problem, and it is recommended to reboot them at least every few days (or whenever network connectivity drops suddenly).